Peer-reviewed Publications |
Bergeron, H., & Gazeau, J. P. (2014). Integral quantizations with two basic examples. Annals of Physics, 344, 43–68.
Résumé: The paper concerns integral quantization, a procedure based on operator-valued measure and resolution of the identity. We insist on covariance properties in the important case where group representation theory is involved. We also insist on the inherent probabilistic aspects of this classical quantum map. The approach includes and generalizes coherent state quantization. Two applications based on group representation are carried out. The first one concerns the Weyl-Heisenberg group and the euclidean plane viewed as the corresponding phase space. We show that a world of quantizations exist, which yield the canonical commutation rule and the usual quantum spectrum of the harmonic oscillator. The second one concerns the affine group of the real line and gives rise to an interesting regularization of the dilation origin in the half plane viewed as the corresponding phase space. (C) 2014 Elsevier Inc. All rights reserved.
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Bergeron, H., Curado, E. M. F., Gazeau, J. P., & Rodrigues, L. M. C. S. (2014). Quantizations from (P)OVM's. J. Phys.: Conf. Ser., 512, 012032.
Résumé: We explain the powerful role that operator-valued measures can play in quantizing any set equipped with a measure, for instance a group (resp. group coset) with its invariant (resp. quasi-invariant) measure. Coherent state quantization is a particular case. Such integral quantizations are illustrated with two examples based on the Weyl-Heisenberg group and on the affine group respectively. An interesting application of the affine quantization in quantum cosmology is mentioned, and we sketch a construction of new coherent states for the hydrogen atom.
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Bergeron, H., Dapor, A., Gazeau, J. P., & Malkiewicz, P. (2014). Smooth big bounce from affine quantization. Physical Review D, 89(8), 083522.
Résumé: We examine the possibility of dealing with gravitational singularities on a quantum level through the use of coherent state or wavelet quantization instead of canonical quantization. We consider the Robertson-Walker metric coupled to a perfect fluid. It is the simplest model of a gravitational collapse, and the results obtained here may serve as a useful starting point for more complex investigations in the future. We follow a quantization procedure based on affine coherent states or wavelets built from the unitary irreducible representation of the affine group of the real line with positive dilation. The main issue of our approach is the appearance of a quantum centrifugal potential allowing for regularization of the singularity, essential self-adjointness of the Hamiltonian, and unambiguous quantum dynamical evolution.
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Bergeron, H., Hrycyna, O., Malkiewicz, P., & Piechocki, W. (2014). Quantum theory of the Bianchi II model. Physical Review D, 90(4), 044041.
Résumé: We describe the quantum evolution of the vacuum Bianchi II universe in terms of the transition amplitude between two asymptotic quantum Kasner-like states. For large values of the momentum variable, the classical and quantum calculations give similar results. The difference occurs for small values of this variable due to the Heisenberg uncertainty principle. Our results can be used, to some extent, as a building block of the quantum evolution of the vacuum Bianchi IX universe.
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Debiossac, M., Zugarramurdi, A., Lunca-Popa, P., Momeni, A., Khemliche, H., Borisov, A. G., & Roncin, P. (2014). Transient Quantum Trapping of Fast Atoms at Surfaces. Phys. Rev. Lett., 112(2).
Résumé: We report on the experimental observation and theoretical study of the bound state resonances in fast atom diffraction at surfaces. In our studies, the He-4 atom beam has been scattered from a high-quality LiF(001) surface at very small grazing incidence angles. In this regime, the reciprocal lattice vector exchange with the surface allows transient trapping of the 0.3-0.5 keV projectiles into the quasistationary states bound by the attractive atom-surface potential well which is only 10 meV deep. Analysis of the linewidths of the calculated and measured resonances reveals that prior to their release, the trapped projectiles preserve their coherence over travel distances along the surface as large as 0.2 μm, while being in average only at some angstroms in front of the last atomic plane.
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Debiossac, M. and Z., A. and Khemliche, H. and Roncin, P. and Borisov, A. G. and Momeni, A. and Atkinson, P. and Eddrief, M. and Finocchi, F. and Etgens, V. H. (2014). Combined experimental and theoretical study of fast atom diffraction on the β2(2×4) reconstructed GaAs(001) surface. Phys. Rev. B, 90(15), 155308.
Résumé: A grazing incidence fast atom diffraction (GIFAD or FAD) setup, installed on a molecular beam epitaxy chamber, has been used to characterize the β2(2×4) reconstruction of a GaAs(001) surface at 530∘C under an As4 overpressure. Using a 400-eV 4He beam, high-resolution diffraction patterns with up to eighty well-resolved diffraction orders are observed simultaneously, providing a detailed fingerprint of the surface structure. Experimental diffraction data are in good agreement with results from quantum scattering calculations based on an ab initio projectile-surface interaction potential. Along with exact calculations, we show that a straightforward semiclassical analysis allows the features of the diffraction chart to be linked to the main characteristics of the surface reconstruction topography. Our results demonstrate that GIFAD is a technique suitable for measuring in situ the subtle details of complex surface reconstructions. We have performed measurements at very small incidence angles, where the kinetic energy of the projectile motion perpendicular to the surface can be reduced to less than 1 meV. This allowed the depth of the attractive van der Waals potential well to be estimated as −8.7 meV in very good agreement with results reported in literature.
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Gauyacq, J. - P., & Lorente, N. (2014). Excitation of bond-alternating spin-1/2 Heisenberg chains by tunnelling electrons. J. Phys. Condens. Matter., 26(39), 394005.
Résumé: Inelastic electron tunneling spectra (IETS) are evaluated for spin-1/2 Heisenberg chains showing different phases of their spin ordering. The spin ordering is controlled by the value of the two different Heisenberg couplings on the two sides of each of the chain's atoms (bond-alternating chains). The perfect anti-ferromagnetic phase, i.e. a unique exchange coupling, marks a topological quantum phase transition (TQPT) of the bond-alternating chain. Our calculations show that the TQPT is recognizable in the excited states of the chain and hence that IETS is in principle capable of discriminating the phases. We show that perfectly symmetric chains, such as closed rings mimicking infinite chains, yield the same spectra on both sides of the TQPT and IETS cannot reveal the nature of the spin phase. However, for finite size open chains, both sides of the TQPT are associated with different IETS spectra, especially on the edge atoms, thus outlining the transition.
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Gauyacq, J. P., & Lorente, N. (2014). Classical limit of a quantal nano-magnet in an anisotropic environment. Surface Science, 630, 325–330.
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Kepenekian, M., Gauyacq, J. - P., & Lorente, N. (2014). Difficulties in the ab initio description of electron transport through spin filters. J. Phys. Condens. Matter., 26(10), 104203.
Résumé: Spin-transport calculations present certain difficulties which are sometimes overlooked when using density-functional theory (DFT) to analyze and predict the behavior of molecular-based devices. We analyze and give examples of some caveats of spintronic calculations using DFT. We first describe how the broken-symmetry problem of DFT can cause serious problems in the evaluation of the spin polarization of electron currents. Next, we signal the low-energy scale of magnetic excitations, which makes them ubiquitous at already rather small biases. The existence of excitations in spin transport has catastrophic consequences in the reliability of the usual transport calculations. Finally, we compare DFT and configuration-interaction calculations of a ferrocene-based double decker that has been heralded as a possible spin-filter, and we cast a word of caution when we show that DFT is qualitatively wrong in the description of both the ground state and the excited states of ferrocene double deckers.
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Kossler, S., Feulner, P., & Gauyacq, J. - P. (2014). Electronic excitations of helium bilayers on a metal substrate. Phys. Rev. B, 89(16), 165410.
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Nave, S., Tiwari, A. K., & Jackson, B. (2014). Dissociative chemisorption of methane on Ni and Pt surfaces: mode-specific chemistry and the effects of lattice motion. J Phys Chem A, 118(41), 9615–9631.
Résumé: The dissociative chemisorption of methane on metal surfaces is of great practical and fundamental interest. Not only is it the rate-limiting step in the steam re-forming of natural gas, but also the reaction exhibits interesting mode-specific behavior and a strong dependence on the temperature of the metal. Electronic structure methods are used to explore this reaction on various Ni and Pt surfaces, with a focus on how the transition state is modified by motion of the metal lattice atoms. These results are used to construct models that explain the strong variation in reactivity with substrate temperature, shown to result primarily from changes in the dissociation barrier height with lattice motion. The dynamics of the dissociative chemisorption of CH4 on Ni and Pt is explored, using a fully quantum approach based on the reaction path Hamiltonian that includes all 15 molecular degrees of freedom and the effects of lattice motion. Agreement with experiment is good, and vibrational excitation of the molecule is shown to significantly enhance reactivity. The efficacy for this is examined in terms of the vibrationally nonadiabatic couplings, mode softening, mode symmetry, and energy localization in the reactive bond.
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Ouvrard, A., Wang, J., Ghalgaoui, A., Nave, S., Carrez, S., Zheng, W., Dubost, H., & Bourguignon, B. (2014). CO Adsorption on Pd(100) Revisited by Sum Frequency Generation: Evidence for Two Adsorption Sites in the Compression Stage. J. Phys. Chem. C, 118(34), 19688–19700.
Résumé: Sum frequency generation (SFG) and low-energy electron diffraction (LEED) have been used to revisit CO adsorption on Pd(100) from very low coverages up to saturation at 300 K Below 0.5 ML, variations of SFG frequency and intensity with coverage are consistent with IRAS results from the literature. Novel observations are done above 0.5 ML, where the CO adlayer compression takes place. The existing compression model postulates the coexistence of compressed and uncompressed CO. We observe two bands in the spectral region of bridge sites and assign them to compressed and uncompressed CO. Both types of CO behave very differently: the molecular hyperpolarizability at compressed sites is smaller by a factor of 2 than at uncompressed sites. The frequency of uncompressed CO red-shifts during compression as the partial coverage decreases, while that of compressed CO continues to blue-shift as coverage increases. In the time domain, the coexistence of compressed and uncompressed sites results in oscillations in the decay of SFG intensity. A strong decrease from 690 to 222 fs of the phase relaxation time of uncompressed CO is observed during compression, indicating a stronger coupling to the substrate. These results are complemented by calculations of dipole-dipole interactions and DFT VASP calculations. While continuing blue-shift of compressed sites reflects a combination of increasing dipolar coupling and chemisorption change with coverage like below 0.5 ML, the very large red-shift amplitude of uncompressed CO indicates a large chemical contribution opposite to compressed CO. DFT VASP calculations allow us to follow the surface structure evolution from 0.5 to 0.67 ML and CO frequency changes with coverage. Pd atoms below compressed CO rows are pushed up, and compressed CO is tilted by 8-90 with respect to the surface normal. A frequency split between compressed and uncompressed CO is found in agreement with experimental data. These results suggest that while compressed CO is less strongly bonded as compression proceeds the remaining uncompressed CO is more strongly bonded.
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